\chapter{Discussion and Conclusion}
\label{sec:DiscussionConclusion}

\section{Conclusion}
\label{sec:ConclusionConclusion}

This research presented a new approach to sketch recognition using PSO. It was noted that the PSO in general improves the accuracy of the final symbol recognition in the system. The use of different preliminary information (speed, time difference and curvature) helps to improve of the PSO algorithm over the original algorithms \cite{CruveDivisionSwarm,PolygonApproximationPSO}. The tradeoff between accuracy achieved and time complexity must be further investigated to achieve better results.  The system introduced an efficient method to sketch recognition using the PSO. The features computed were a hybrid set of a stroke based features which gives more information on the geometrical and structure of the shape tested.  

The system was tested on three different datasets, simple presentation symbols, electrical symbols and logic design dataset. The number and the complexity of symbols recognized by the system varied from simple to complex but did not affect the final recognition of the system. Tests performed confirmed that PSO achieve better performance and optimization than other algorithms. In general \textsl{ALS2} proved to generate the best result on different datasets. Algorithm \textsl{ALS2} achieved better segmentation results than any other algorithm in shapes that are combination of curves and lines as in digital design dataset. Algorithm \textsl{ALS1} achieves high performance in electrical symbols but gives poor results in logic design set. The result is justifiable because logic design dataset contains symbols that are differentiated by number of curves in OR-gate and XOr gate, therefore representing the symbol as lines will remove important information. 

The system uses different sets of features that represent shape geometrical and global properties. Literature review showed that system that relies only on global shape properties fails to identify the shapes that have small geometrical difference (ie. Xor gate and Nor gate). Using geometrical and stroke based features with the global shape properties helps to improve the final recognition rate.     



%The system still has drawback as it lack in handling over traced strokes.  Another drawback is that until now we only applied the system to single symbols.  Full free hand sketch test has not been applied on the system. %sketched 
%drawback of the system is that it takes more time to segment strokes in comparison with other similar algorithms.

\newpage

\section{Future Work}
\label{sec:FutureWork}


%As you can see form the experiments PSO have proved a spuriously than other system. 
%\section{Future Work}
The system still has some drawbacks; it needs to be improved to handle over traced strokes. Another improvement required is handling of multiple symbols since we only applied the system to single symbols. In addition, full free hand sketch test has not been applied on the system. %sketched 

Hence, the next step in this research is to complete the clustering algorithm for fully automated sketch recognition. This will enable testing the system for more than single symbol at a time. The segmentation algorithm may be more powerful if it can segment the stroke into more types of primitives other than the line and curve categorization used in this work. Other area of modification can be the features extraction and classifier. Adding few more spatial and structure features should improve classifications. After segmenting the stroke the system can generate a structural graph from segments and there spatial relations. This graph will be matched with the set of known symbol template to make the identification. Those results along with the SVM classifier results are expected to enhance the system as a whole and achieve even better recognition rates.  %Each new stroke is checked if it can be a symbol or is a part of already drawn un completed symbol.  



%drawback of the system is that it takes more time to segment strokes in comparison with other similar algorithms.

\appendix
\chapter{Appendix: Step by Step Example Details}
%\addcontentsline{toc}{chapter}{Appendix: Step by Step Example Details}
\chaptermark{Appendix}
\markboth{Appendix}{Appendix}
\label{ChapterstepExample}%\chapter{Step by Step Example}
%In this chapter a step by step example is presented to clarify the presented system. Let us make an assumption that the user will draw a clock using two strokes. Figure \ref{fig:clock} show the two strokes and how the user draws them. The next steps demonstrate how output of the system after each step. The first section \ref{sec:stepseg} describe how the segmentation is done step by step. Section \ref{sec:steprec} shows the details of feature calculation and the classification process. 

\section{Step by Step Segmentation}
\label{apsec:stepseg}

In this step the user draw one or more stroke to draw a symbol. Figure \ref{fig:clock} illustrate the sequence and direction of user draw. In this section, each stroke user draw will be labeled as it illustrated in Figure \ref{fig:clockstroke1} and Figure \ref{fig:clockstroke2} .  Table \ref{tab:StepsStroke1Details} shows the detailed output of the program at each step. The input of this step is the stroke points and the output is a list of segments that will be used in the recognition process. The algorithm that computes the segmentation is demonstrated as follows:

%\begin{enumerate}

%\item Extracting $P_dp$ as in Section \ref{sec:Preprocessing} and Algorithm \ref{extractpdp}
\begin{algorithm}
\caption{Extracting $P_dp$}
\label{extractpdp}
\begin{verbatim}
  1. For each point in Stroke do the following:
  		1.a Compute distance from previous point.
  		1.b Compute Time difference from previous point and add it to Time_list.  
  		1.c Compute Velocity and add it to Vel_list. 
  		1.d Compute Direction and add it to Dir_list.
  	 	1.e Compute Curvature and add it to Cur_list.(Eq.4.1) 
  	end (for loop)
  2. For each  list computed in previous step do the follwing:   
  	 2.a Compute average of all points. 
  	 2.b set average as threshold.  
  	 2.c Create region from continuous points larger than threshold. 
  	 2.d for each region do the following. 
  	 	   2.d.1 find the maximum 
  	 	   2.d.1 Add point to P_dp 
  	  end
     end 
\end{verbatim}	
\end{algorithm}
%\item Ellipse Fitting: which is an attempt to fit as an ellipse as in Section \ref{sec:EllipseDetection} 
%he axes of the ellipse are estimated as the $width/2$ and $height/2$ of the stroke bounding box where $width$ is width and $height$ is height of the bonding box.
\begin{algorithm}
\caption{Ellipse Fitting Algorithm}
\label{ellipseFitAlg}
\begin{verbatim}
1. Initialize the axes of ellipse and center by bounding box information
2. Repeat the following for few loops: 
	2.a Compute error in Equation  4.2 
	2.b Update center of ellipse and axis from error. 
3. Compute percent in Equation 4.4 
4. Computer eff in Equation 4.3 
5. if eff < 0.2  then fit as ellipse otherwise move to segment. 
\end{verbatim}	
\end{algorithm}
%\item Segmentation ALS1 as explained in Section \ref{sec:SwarmSegmentation}. The algorithm will be similar to the PSO algorithm in section \ref{sec:ParticleSwarmAlgorithm}. 
 
\begin{algorithm}
\caption{ First Swarm Algorithm}
\label{AlgS1alg}
\begin{verbatim}
Initialize 
  1. Generate N particles with M dimensions (P_i...P_N) 
  2. Generate velocities for each particle for M dimension randomly. 
  3. Repeat till Maximum number of iteration OR Error Threshold  
         For each particle P_i do the following 
         3.a   Compute fitness  (fitness) 
         				3.a.1 Compute the Error of approximation as in Eq.4.5
         				3.a.2. Computer the fitness function as in Eq. 4.4 
         3.b   Determine Lbest  
               if (lbest_fitness<fitness)
                  3.b.1   lbest=P_i
         3.c      Determine Gbest.
               if (lGest_fitness<fitness)
                  3.c.1   lGest=P_i
         3.d   Compute the Velocity for each dimension using Eq.3.2 
         3.e   Bound Velocity using Eq.3.4
         3.f   Update particle values using Eq. 3.3
         3.g   Refine the location of the particle 
         end .
     end 
4. return Gbest
\end{verbatim}
\end{algorithm}	
%\item Segmentation ALS2  as explained in Section \ref{sec:PolygonDivisionAlgorithm}
\begin{algorithm}
\caption{ Second Swarm Algorithm}
\label{AlgS2alg}
\begin{verbatim}
Initialize 
  1. Generate N particles with M dimensions (P_i...P_N) 
  2. Generate velocities for each particle for M dimension randomly. 
  3. Repeat till Maximum number of iteration OR Error Threshold  
         For each particle P_i do the following 
         3.a   Compute fitness  (fitness) 
              3.a.1 For each Segment in the particle do the following
         				    3.a.1.I   Error of approximation as Line (Eq. 4.7 - 4.9 )
         			      3.a.1.II  Error of approximation as circular arc (Eq. 4.10 - 4.19 )
         				    3.a.1.III Computer minimum of both approximation 
         			3.a.2 Compute Error of the particle as in Eq.  4.20
         			3.a.3 Compute fitness of the particle as in Eq. 4.21
         3.b   Determine Lbest  
               if (lbest_fitness<fitness)
                  3.b.1   lbest=P_i
         3.c      Determine Gbest.
               if (lGest_fitness<fitness)
                  3.c.1   lGest=P_i
         3.d   Compute the Velocity for each dimension using Eq.3.2 
         3.e   Bound Velocity using Eq.3.4
         3.f   Update particle values using Eq. 3.3
         3.g   Refine the location of the particle 
         end .
     end 
4. return Gbest
\end{verbatim}	
\end{algorithm}	

\begin{landscape}
\begin{scriptsize}
%\begin{table}
	%\centering 
%\scalebox{0.6}{		
\begin{longtable}{|p{2cm}|p{2cm}|p{2cm}|p{2cm}|p{13cm}|}
\caption{Detailed Output of System in Each Step of Segmentation}
\label{tab:StepsStroke1Details} \\

\hline 
\multicolumn{1}{|p{2cm}|}{\textbf{Step}} & 
\multicolumn{1}{p{2cm}|}{\textbf{Description}} &
\multicolumn{1}{p{2cm}|}{\textbf{Inputs}} &
\multicolumn{1}{p{2cm}|}{\textbf{Details}} &
\multicolumn{1}{p{13cm}|}{\textbf{Output}} 
\\ \hline 
\endfirsthead


\multicolumn{3}{c}%
{{\bfseries \tablename\ \thetable{} -- continued from previous page}} \\
\hline 
\multicolumn{1}{|p{2cm}|}{\textbf{Step}} & 
\multicolumn{1}{p{2cm}|}{\textbf{Description}} &
 \multicolumn{1}{p{2cm}|}{\textbf{Inputs}} &
 \multicolumn{1}{p{2cm}|}{\textbf{Details}} &
 \multicolumn{1}{p{13cm}|}{\textbf{Output}} 
\\ \hline 
\endhead


 
%Step & Description of Step & Input & Steps & Output \\ \hline
Stroke 1 & Extracting point and computing boundary data & -- &  see Section \ref{sec:Preprocessing} & 
\begin{scriptsize}
Stroke has 62 points = [P(198.0,153.0), P(197.0,150.0), P(197.0,145.0), P(198.0,140.0), P(203.0,125.0), P(205.0,120.0) , P(205.0,117.0), P(210.0,111.0) , P(214.0,103.0) , P(219.0,97.0), P(225.0,89.0) , P(229.0,85.0) , P(242.0,77.0) , P(247.0,73.0) , P(275.0,64.0) , P(287.0,62.0) , P(325.0,62.0) , P(333.0,63.0) , P(362.0,68.0) , P(372.0,72.0) , P(391.0,77.0) , P(406.0,83.0) , P(424.0,91.0) , P(440.0,100.0), P(474.0,133.0) , P(485.0,149.0) , P(492.0,164.0) , P(499.0,182.0) , P(501.0,191.0) , P(501.0,207.0) , P(499.0,222.0) , P(496.0,239.0) , P(471.0,292.0) , P(467.0,302.0) , P(456.0,315.0) , P(441.0,329.0) , P(427.0,339.0) , P(418.0,344.0) , P(398.0,354.0) , P(336.0,371.0) , P(283.0,376.0) , P(263.0,378.0) , P(242.0,378.0) , P(232.0,376.0) , P(213.0,373.0) , P(194.0,367.0) , P(177.0,362.0) , P(138.0,343.0) , P(129.0,336.0) , P(124.0,331.0) , P(120.0,321.0) , P(115.0,310.0) , P(113.0,297.0) , P(112.0,284.0) , P(114.0,256.0) , P(121.0,219.0) , P(128.0,202.0) , P(137.0,184.0) , P(143.0,172.0) , P(154.0,161.0) , P(172.0,146.0) , P(172.0,146.0)]

 Bonding box is  = Corner P(112.0, 62.0), w= 389.0, h=  316.0
 number of point in this stroke is   62
\end{scriptsize}
 \\ \hline
Possible Dominate point Extraction & for Computing details see Section\ref{sec:Preprocessing} &  Stroke points  &   &    Number of $P_{dp}$  = 11
 Pdp = [ 2 (197.0 , 145.0 ), 4 (203.0 , 125.0 ), 3 (198.0 , 140.0 ), 22 (424.0 , 91.0 ), 19 (372.0 , 72.0 ), 26 (492.0 , 164.0 ), 28 (501.0 , 191.0 ), 9 (219.0 , 97.0 ), 31 (496.0 , 239.0 ), 0 (198.0 , 153.0 ), 41 (263.0 , 378.0 )]

\\ \hline 
Segmentation & Segmentation of Ellipse & $P_{dp}$   &  Ellipse fitting  & 
 
  The circle is   a = 103.05715108084719 ,b = 103.06851874747797 , Center( 283.03365107691775,  181.05035287667172 )   with Error =  1.9471676673301757 , Percent =1.0695193086531243
eff  = 0.27463462099275116  
 Ellipse detected... 
 
 \\ \hline
 
Stroke 2 & Extracting point and computing boundary data & -- &  see Section \ref{sec:Preprocessing} &
\begin{scriptsize}
Stroke has 205 points = [P(201.0,179.0) , P(202.0,180.0) , P(202.0,182.0) , P(202.0,185.0) , P(202.0,187.0) , P(202.0,190.0) , P(202.0,192.0) , P(202.0,196.0) , P(202.0,202.0) , P(201.0,206.0) , P(200.0,219.0) , P(198.0,231.0) , P(198.0,234.0) , P(198.0,238.0) , P(197.0,244.0) , P(197.0,248.0) , P(197.0,251.0) , P(196.0,258.0) , %P(196.0,260.0) , P(196.0,263.0) , P(195.0,265.0) , P(195.0,266.0) , P(195.0,269.0) , P(195.0,271.0) , P(195.0,273.0) , P(195.0,278.0) , P(195.0,279.0) , P(195.0,281.0) , P(195.0,282.0) , P(195.0,284.0) , P(195.0,285.0) , P(195.0,288.0) , P(195.0,290.0) , P(195.0,295.0) , P(195.0,297.0) , P(195.0,298.0) , P(196.0,298.0) , P(196.0,299.0) , P(196.0,300.0) , P(196.0,301.0) , P(197.0,301.0) , P(198.0,301.0) , P(200.0,301.0) , P(203.0,301.0) , %P(206.0,301.0) , P(208.0,301.0) , P(213.0,301.0) , P(217.0,302.0) , P(219.0,302.0) , P(223.0,303.0) , P(234.0,304.0) , P(237.0,304.0) , P(240.0,306.0) , P(246.0,306.0) , P(247.0,307.0) , P(248.0,307.0) , P(249.0,307.0) , P(250.0,307.0) , P(250.0,306.0) , P(250.0,305.0) , P(250.0,304.0) , P(250.0,302.0) , P(251.0,299.0) , P(251.0,296.0) , P(251.0,294.0) , P(251.0,289.0) , P(252.0,285.0) , P(253.0,279.0) , P(253.0,274.0) , P(253.0,271.0) , P(253.0,264.0) , P(253.0,257.0) , P(254.0,252.0) , P(254.0,241.0) , P(254.0,237.0) , P(255.0,232.0) , P(255.0,229.0) , P(255.0,225.0) , P(256.0,212.0) , P(256.0,209.0) , P(256.0,206.0) , P(257.0,205.0) , P(257.0,200.0) , P(257.0,197.0) , P(258.0,195.0) , P(258.0,194.0) , P(258.0,189.0) , P(258.0,187.0) , P(258.0,186.0) , P(259.0,184.0) , P(259.0,181.0) , P(259.0,179.0) , P(259.0,178.0) , P(260.0,176.0) , P(260.0,174.0) , P(260.0,173.0) , P(260.0,172.0) , P(260.0,171.0) , P(260.0,169.0) , P(260.0,168.0) , P(260.0,167.0) , P(261.0,166.0) , P(261.0,165.0) , P(261.0,164.0) , P(261.0,162.0) , P(262.0,162.0) , P(263.0,162.0) , P(264.0,162.0) , P(268.0,162.0) , P(275.0,162.0) , P(279.0,162.0) , P(289.0,162.0) , P(291.0,162.0) , P(301.0,163.0) , P(305.0,164.0) , P(312.0,164.0) , P(315.0,165.0) , P(318.0,165.0) , P(319.0,165.0) , P(319.0,166.0) , P(320.0,168.0) , P(320.0,171.0) , P(320.0,173.0) , P(320.0,176.0) , P(321.0,182.0) , P(321.0,191.0) , P(322.0,198.0) , P(322.0,211.0) , P(323.0,226.0) , P(324.0,229.0) , P(324.0,238.0) , P(324.0,263.0) , P(325.0,272.0) , P(325.0,281.0) , P(325.0,288.0) , P(325.0,291.0) , P(325.0,297.0) , P(325.0,299.0) , P(325.0,301.0) , P(325.0,305.0) , P(324.0,306.0) , P(324.0,307.0) , P(323.0,308.0) , P(324.0,307.0) , P(325.0,307.0) , P(328.0,306.0) , P(332.0,306.0) , P(339.0,306.0) , P(347.0,305.0) , P(354.0,304.0) , P(365.0,304.0) , P(376.0,304.0) , P(379.0,304.0) , P(385.0,304.0) , P(391.0,304.0) , P(392.0,304.0) , P(393.0,304.0) , P(393.0,302.0) , P(393.0,301.0) , P(394.0,297.0) , P(394.0,290.0) , P(393.0,284.0) , P(393.0,274.0) , P(392.0,258.0) , P(391.0,245.0) , P(391.0,233.0) , P(389.0,213.0) , P(388.0,198.0) , P(388.0,189.0) , P(388.0,184.0) , P(388.0,178.0) , P(388.0,177.0) , P(388.0,176.0) , P(388.0,174.0)
.................................................................................................................. .................................................................................  , P(388.0,173.0) , P(388.0,171.0) , P(388.0,170.0) , P(388.0,168.0) , P(388.0,167.0) , P(388.0,166.0) , P(388.0,165.0) , P(389.0,165.0) , P(390.0,165.0) , P(395.0,165.0) , P(401.0,165.0) , P(406.0,165.0) , P(418.0,166.0) , P(424.0,167.0) , P(426.0,167.0) , P(429.0,167.0) , P(430.0,167.0) , P(431.0,167.0) , P(432.0,167.0) , P(433.0,169.0) , P(434.0,170.0) , P(434.0,174.0) , P(436.0,185.0) , P(440.0,200.0) , P(442.0,220.0) , P(442.0,224.0) , P(446.0,267.0) , P(447.0,279.0) , P(448.0,286.0) , P(448.0,287.0) , P(448.0,287.0)]

 Bonding box is  = Corner P(195.0, 162.0), w= 253.0, h=  146.0
 \end{scriptsize}
  \\ \hline
  & Possible Dominate point Extraction for details see Section\ref{sec:Preprocessing} &  Stroke points  & 1. compute the $P_{pd}$  & \begin{scriptsize}   Number of $P_{pd}$  =  36

 Pdp = [ 25 (195.0 , 278.0 ), 30 (195.0 , 285.0 ), 33 (195.0 , 295.0 ), 27 (195.0 , 281.0 ), 34 (195.0 , 297.0 ), 46 (213.0 , 301.0 ), 47 (217.0 , 302.0 ), 50 (234.0 , 304.0 ), 28 (195.0 , 282.0 ), 94 (260.0 , 174.0 ), 93 (260.0 , 176.0 ), 95 (260.0 , 173.0 ), 98 (260.0 , 169.0 ), 48 (219.0 , 302.0 ), 99 (260.0 , 168.0 ), 109 (275.0 , 162.0 ), 113 (301.0 , 163.0 ), 94 (260.0 , 174.0 ), 132 (325.0 , 272.0 ), 136 (325.0 , 297.0 ), 112 (291.0 , 162.0 ), 137 (325.0 , 299.0 ), 110 (279.0 , 162.0 ), 144 (325.0 , 307.0 ), 147 (339.0 , 306.0 ), 150 (365.0 , 304.0 ), 132 (325.0 , 272.0 ), 168 (388.0 , 189.0 ), 171 (388.0 , 177.0 ), 174 (388.0 , 173.0 ), 146 (332.0 , 306.0 ), 175 (388.0 , 171.0 ), 183 (395.0 , 165.0 ), 186 (418.0 , 166.0 ), 169 (388.0 , 184.0 ), 191 (431.0 , 167.0 ) ] 

  \end{scriptsize}
    \\ \hline
 \\ \hline 
Segmentation & Segmentation of Ellipse & $P_{dp}$   &  Ellipse fitting  & 
  The Ellipse is   a = 125.5 ,b = 125.5 , Center( 320.5,  235.0 )   with Error =  7.074966523515405 , Percent =1.1481777694994926 certainty  =  0.08114368920921669  
 \\ \hline
 Segmentation & PSO Segmentation ALgS1 & $P_{dp}$  & ALgS1 (result if Figure \ref{fig:Stroke2Seg1labeled} ) & 
Iteration 0 the global best fitness is 0.7 and error value is 675.0457637480733  and the particle is  Particles =  [  1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ] 
Iteration 10 the global best fitness is 0.7777777777777778 and error value is 719.5716152204503  and the particle is  Particles =  [  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ] 
Iteration 20 the global best fitness is 0.7777777777777778 and error value is 719.5716152204503  and the particle is  Particles =  [  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ] 
 After swarm  the global best fitness is 0.875 and error value is 729.248312158671  and the particle is  Particles =  [  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ] 
  
 F First Polygonization PSO = [ S0 Line[P(226.0,139.0) to P(241.0,209.0)]  ,      S1 Line[P(241.0,209.0) to P(266.0,226.0)]  ,      S2 Line[P(266.0,226.0) to P(296.0,128.0)]  ,      S3 Line[P(296.0,128.0) to P(312.0,216.0)]  ,    ]  
 \\ \hline 
 
  Segmentation & PSO Segmentation ALgS2 & $P_{dp}$  & ALgS2  (result if Figure \ref{fig:Stroke2Seg2labeled} )&    
 Iteration 0 the global best fitness is 8.725462920280576E-11 and error value is 9.151490748550003  and the particle is  Particles =  [  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ]
 
Iteration 10 the global best fitness is 3.126281513587432E-7 and error value is 8.61499750333895  and the particle is  Particles =  [  1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ]
 
Iteration 20 the global best fitness is 3.126281513587432E-7 and error value is 8.61499750333895  and the particle is  Particles =  [  1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ]
 
 After swarm  the global best fitness is 3.126281513587432E-7 and error value is 8.61499750333895  and the particle is  Particles =  [  1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ] 
 
  second PSO =   Segments = [   S0 Line{P(226.0,139.0) to P(238.0,183.0)},      S1 Line{P(238.0,183.0) to P(241.0,213.0)},      S2 Line{P(241.0,213.0) to P(276.0,227.0)},      S3 Line{P(276.0,227.0) to P(287.0,144.0)},      S4 Curve{P(287.0,144.0) to P(310.0,131.0),  Center ( 299.02634312229503,137.80386092517725) Radius =11.907214051459519 },  S5 Curve{P(310.0,131.0) to P(312.0,216.0),  Center ( 82.44520390380922,172.2089170470769) Radius =231.70851748053468 },  S6 Line{P(312.0,216.0) to P(336.0,224.0)}, ]  
  
 
 \\ \hline 
Choosing best fit & Compare between ALgS1 and AlgS2 &  First PSO and Second PSO  &  (result if Figure \ref{fig:FinalSegmentation} ) & 
   The error ALgS1 780.6652975044847  Algs2 161.60692855994625    Best = ALgS2  \\ \hline 
 
 
		\end{longtable}
%}



%\end{table}

\end{scriptsize}

\end{landscape}


\begin{figure}
	\centering
	\subfigure [AlgS1 Output]{
		\includegraphics{afterDefense/Stroke2Seg1labeled.jpg.eps}
	\label{fig:Stroke2Seg1labeled}}
	
	\subfigure[AlgS2 Output]{	\includegraphics{afterDefense/Stroke2Seg2labeled.jpg.eps}	\label{fig:Stroke2Seg2labeled}
	}
	\subfigure[Final Segmentation of Symbol]{		\label{fig:FinalSegmentation}	\includegraphics[scale=0.65]{afterDefense/FinalSegmentation.jpg.eps}
	}
	\caption{Segmentation Outputs For Second Stroke}
\end{figure}
 

The final output of this step is list $L_s$ of segments There are  9  segments in this symbol

\begin{itemize}
	\item    Segment S0  = Ellipse ( Stroke 1)
   \item Segment S1  =   Line ( Stroke 2)
     \item  Segment S2 = Line ( Stroke 2)
     \item  Segment S3  =  Line ( Stroke 2)
     \item Segment S4  =   Line ( Stroke 2)
  \item    Segment S5  =  Curve  ( Stroke 2)
     \item  Segment S6  =  Curve  ( Stroke 2)
     \item  Segment S7  =  Line   ( Stroke 2)
     \item  Segment S8  =  Line   ( Stroke 2)
\end{itemize}

\section{Step by Step Recognition}
\label{apsec:steprec}

\begin{figure}
	\centering
		\includegraphics[scale=0.85]{afterDefense/FinalSegmentation.jpg.eps}
	\caption{Best Segmentation }
	\label{fig:segmentatiofinal.jpg}
\end{figure}

%\begin{enumerate}
%\begin{itemize}

	The input of the step is the list of segmentation $L_s$ that is used to compute the feature vector. Figure \ref{fig:segmentatiofinal.jpg} shows the best segmentation as given by the previous step. This step can be summarized as firstly using $L_s$ to computer the feature vector and then introduce this vector the SVM classifier to classify it to one of the trained categories. The details of each step of feature extraction are detailed in the next algorithm. Feature extraction step is divided into four steps where each feature set is computed separately then all sets are appended to construct a final feature vector. 
	\begin{enumerate}
	\item Computing Structural and geometrical Features(FS1). This step computes number of parallel, perpendicular line and similar structural features [13 features]. Algorithm \ref{FeatureAlg} in Appendix \ref{ChapterstepExample}  is used to determine these features.
 	\item Rubine Feature Set (FS2) [12 features] .  Compute Rubine features as in \cite{gestureexample12} 
	\item Statistical Features (FS3) compute the moments as in \cite{zernike61} for N=10 there are 32 features.
	\item Global shape properties set (FS4). Firstly compute the convex hull of the stroke points then compute the rest of the features [13 features]. 
	\item Introduce the computed feature vector (All 70 features) to the classifier and check the label of the detected symbol. 
\end{enumerate}

	 \begin{algorithm}
\caption{Computing Structural Features}
\label{FeatureAlg}
	\begin{verbatim}
Initialize 
  1. For each segment Si in list Ls  do the following. 
      1.a If segment si is a line do the following 
            1.a.I. Compute the slope and intercept of line si. 
            1.a.II Increment Parallel count  if 
                  parallel with each other line in Ls
            1.a.III Increment PerpendicularCount if 
                    perpendicular with each other line in Ls 
            1.a.IV Increment Intersection Count if 
                    intersected with any other line. 
                    1.a.II.A  if Intersection found determine 
                              type of intersection or (X,T,L)
      1.b If segment si is curve do the following. 
          1.b.I Increment Intersect if
               Intersect other line or curve
    1.b.II Increment number 
                 of curves and primitives. 
4. return Feature_Vector_FS1
\end{verbatim}	
 \end{algorithm}

\begin{landscape}
\begin{scriptsize}
	
 \begin{longtable}{|p{2cm}|p{2cm}|p{2cm}|p{2cm}|p{13cm}|}
\caption{Detailed Output of System in Each Step of Recognition}
\label{tab:StepsRegDetails} \\

\hline 
\multicolumn{1}{|p{2cm}|}{\textbf{Step}} & 
\multicolumn{1}{p{2cm}|}{\textbf{Description}} &
\multicolumn{1}{p{2cm}|}{\textbf{Inputs}} &
\multicolumn{1}{p{2cm}|}{\textbf{Details}} &
\multicolumn{1}{p{13cm}|}{\textbf{Output}} 
\\ \hline 
\endfirsthead


\multicolumn{3}{c}%
{{\bfseries \tablename\ \thetable{} -- continued from previous page}} \\
\hline 
\multicolumn{1}{|p{2cm}|}{\textbf{Step}} & 
\multicolumn{1}{p{2cm}|}{\textbf{Description}} &
 \multicolumn{1}{p{2cm}|}{\textbf{Inputs}} &
 \multicolumn{1}{p{2cm}|}{\textbf{Details}} &
 \multicolumn{1}{p{13cm}|}{\textbf{Output}} 
\\ \hline 
\endhead

 Feature Extraction of FS1 & Preprocessing of Structural Featues  &   There are  9  segments in this symbol $L_s$ = 
   Segment S0  = Ellipse
   Segment S1  = Line
   Segment S2  = Line
   Segment S3  = Line
   Segment S4  = Line
   Segment S5  = Curve
   Segment S6  = Curve
   Segment S7  = Line
   Segment S8  = Line  &  (see First Algorithm in Section \ref{sec:steprec} )  &    Line from  24 x= 241.0y=213.0  to 49 x2= 276.0y2=227.0  is\textbf{ parallel} to Line from  163 x= 312.0y=216.0  to 185 x2= 336.0y2=224.0
 
 Line from  0 x= 226.0y=139.0  to 14 x2= 238.0y2=183.0 \textbf{ intersects }Line from  14 x= 238.0y=183.0  to 24 x2= 241.0y2=213.0
 
 Line from  0 x= 226.0y=139.0  to 14 x2= 238.0y2=183.0  \textbf{intersects} Line from  24 x= 241.0y=213.0  to 49 x2= 276.0y2=227.0
 
 Line from  0 x= 226.0y=139.0  to 14 x2= 238.0y2=183.0 \textbf{ intersects} Line from  49 x= 276.0y=227.0  to 98 x2= 287.0y2=144.0
 
 Line from  0 x= 226.0y=139.0  to 14 x2= 238.0y2=183.0\textbf{  intersects }Line from  163 x= 312.0y=216.0  to 185 x2= 336.0y2=224.0
 
 Line from  0 x= 226.0y=139.0  to 14 x2= 238.0y2=183.0 \textbf{ intersects} Line from  185 x= 336.0y=224.0  to 223 x2= 344.0y2=137.0
 %Line from  14 x= 238.0y=183.0  to 24 x2= 241.0y2=213.0  intersects Line from  24 x= 241.0y=213.0  to 49 x2= 276.0y2=227.0
 %Line from  14 x= 238.0y=183.0  to 24 x2= 241.0y2=213.0  intersects Line from  49 x= 276.0y=227.0  to 98 x2= 287.0y2=144.0
 %Line from  14 x= 238.0y=183.0  to 24 x2= 241.0y2=213.0  intersects Line from  163 x= 312.0y=216.0  to 185 x2= 336.0y2=224.0
 %Line from  14 x= 238.0y=183.0  to 24 x2= 241.0y2=213.0  intersects Line from  185 x= 336.0y=224.0  to 223 x2= 344.0y2=137.0
 %Line from  24 x= 241.0y=213.0  to 49 x2= 276.0y2=227.0  intersects Line from  49 x= 276.0y=227.0  to 98 x2= 287.0y2=144.0
 %Line from  24 x= 241.0y=213.0  to 49 x2= 276.0y2=227.0  intersects Line from  163 x= 312.0y=216.0  to 185 x2= 336.0y2=224.0
 %Line from  24 x= 241.0y=213.0  to 49 x2= 276.0y2=227.0  intersects Line from  185 x= 336.0y=224.0  to 223 x2= 344.0y2=137.0
 %Line from  49 x= 276.0y=227.0  to 98 x2= 287.0y2=144.0  intersects Line from  163 x= 312.0y=216.0  to 185 x2= 336.0y2=224.0
 
 Line from  49 x= 276.0y=227.0  to 98 x2= 287.0y2=144.0  intersects Line from  185 x= 336.0y=224.0  to 223 x2= 344.0y2=137.0
 
 Line from  163 x= 312.0y=216.0  to 185 x2= 336.0y2=224.0  intersects Line from  185 x= 336.0y=224.0  to 223 x2= 344.0y2=137.0  

\\ \hline 


 FS1 & Structural and geometrical Features & Segment List $L_s$  &  & 
 The final Feature vector of the FS1==>
  Number of primitives 3.0   ,    Feature Number of segments 9.0   ,    Feature Line count 6.0   ,    Feature Curves Count 3.0   ,    Feature Ellipse Count 1.0   ,    Feature Intersection T type -1.0   ,    Feature Intersection L type 4.0   ,    Feature Intersection X type -1.0   ,    Feature Parallel Count 1.0   ,    Feature PerPendicular Count -1.0   ,    Feature Intersection Lines Count 4.0   ,    Feature Min Radius 1.7976931348623157E308   ,    Feature Max Radius 231.70851748053468   
 
 \\ \hline
FS2  & Rubine Features & Segment List $L_s$  &   see \cite{gestureexample12}   & 
\begin{scriptsize}
 Feature Rubine 0 -1.0   ,    Feature Rubine 1 -1.0   ,    Feature Rubine 2 477.6107201476952   ,    Feature Rubine 3 0.6368010415482491   ,    Feature Rubine 4 169.49926253526885   ,    Feature Rubine 5 0.8908593331996381   ,    Feature Rubine 6 0.454279262624981   ,    Feature Rubine 7 1179.0172885029808   ,    Feature Rubine 8 4.712388980384688   ,    Feature Rubine 9 70.80157037633609   ,    Feature Rubine 10 55.4044569978846   ,    Feature Rubine 11 9.140625   ,    Feature Rubine 12 41783.0   ,   
\end{scriptsize}
 \\ \hline
 
FS3 & Momments Computation   &  Segment List $L_s$  &  see \cite{zernike61}  &

\begin{scriptsize}
   Feature Zernike moments 0 158.87520185460517   ,    Feature Zernike moments 0 7.007557168632727   ,    Feature Zernike moments 1 34.26844061831789   ,    Feature Zernike moments 1 6.658086415801404   ,    Feature Zernike moments 2 85.70032052974454   ,    Feature Zernike moments 2 9.441591321498212   ,    Feature Zernike moments 3 11.73170471301825   ,    Feature Zernike moments 3 66.52997844880663   ,    Feature Zernike moments 4 20.42774127507497   ,    Feature Zernike moments 4 10.196341027811322   ,    Feature Zernike moments 5 52.821799077785066   ,    Feature Zernike moments 5 12.078236804336935   ,    Feature Zernike moments 6 27.748912050714   ,    Feature Zernike moments 6 9.870152472028517   ,    Feature Zernike moments 7 26.079803494397133   ,    Feature Zernike moments 7 28.109003184347657   ,    Feature Zernike moments 8 23.32097186060531   ,    Feature Zernike moments 8 7.632681250023639   ,    Feature Zernike moments 9 6.5841386188472395   ,    Feature Zernike moments 9 51.34195037191517   ,    Feature Zernike moments 10 30.122054353503337   ,    Feature Zernike moments 10 26.902895199361584   ,    Feature Zernike moments 11 1.8295982451659387   ,    Feature Zernike moments 11 29.93196640188875   ,    Feature Zernike moments 12 64.0879253626976   ,    Feature Zernike moments 12 31.811780133580722   ,    Feature Zernike moments 13 23.614051070558084   ,    Feature Zernike moments 13 1.8043229719502216   ,    Feature Zernike moments 14 113.92181136864328   ,    Feature Zernike moments 14 67.26888519955787   ,    Feature Zernike moments 15 47.7397132180995   ,    Feature Zernike moments 15 31.490125533238682   ,    Feature Zernike moments 16 10.320112066817984   ,    Feature Zernike moments 16
\end{scriptsize}
  
  \\ \hline
FS4   &  &Segment List $L_s$   &  &  \begin{scriptsize} 
 The convex hull    [ X = 383.0   Y = 146.0  Time = 1250452568824,  X = 380.0   Y = 139.0  Time = 1250452568816,  X = 368.0   Y = 119.0  Time = 1250452568800,  X = 363.0   Y = 113.0  Time = 1250452568792,  X = 352.0   Y = 101.0  Time = 1250452568776,  X = 348.0   Y = 97.0  Time = 1250452568768,  X = 342.0   Y = 92.0  Time = 1250452568760,  X = 335.0   Y = 88.0  Time = 1250452568752,  X = 329.0   Y = 85.0  Time = 1250452568744, % X = 322.0   Y = 83.0  Time = 1250452568736,  X = 302.0   Y = 78.0  Time = 1250452568728,  X = 293.0   Y = 77.0  Time = 1250452568720,  X = 282.0   Y = 76.0  Time = 1250452568712,  X = 250.0   Y = 76.0  Time = 1250452568688,  X = 239.0   Y = 77.0  Time = 1250452568680,  X = 229.0   Y = 79.0  Time = 1250452568672,  X = 220.0   Y = 81.0  Time = 1250452568664,  X = 217.0   Y = 83.0  Time = 1250452568656,  X = 201.0   Y = 96.0  Time = 1250452568648,  X = 196.0   Y = 103.0  Time = 1250452568640,  X = 186.0   Y = 118.0  Time = 1250452568624,  X = 182.0   Y = 127.0  Time = 1250452568608,  X = 180.0   Y = 209.0  Time = 1250452569139,  X = 180.0   Y = 247.0  Time = 1250452569092,  X = 181.0   Y = 253.0  Time = 1250452569080,  X = 185.0   Y = 260.0  Time = 1250452569073,  X = 190.0   Y = 265.0  Time = 1250452569056,  X = 194.0   Y = 267.0  Time = 1250452569047,  X = 213.0   Y = 274.0  Time = 1250452569031,  X = 220.0   Y = 276.0  Time = 1250452569023,  X = 256.0   Y = 284.0  Time = 1250452568995,  X = 266.0   Y = 284.0  Time = 1250452568976,  
 ...................................................X = 274.0   Y = 283.0  Time = 1250452568969,  X = 282.0   Y = 281.0  Time = 1250452568960,  X = 290.0   Y = 278.0  Time = 1250452568952,  X = 298.0   Y = 274.0  Time = 1250452568944,  X = 319.0   Y = 262.0  Time = 1250452568936,  X = 339.0   Y = 243.0  Time = 1250452568912,  X = 357.0   Y = 222.0  Time = 1250452568889,  X = 368.0   Y = 202.0  Time = 1250452568872,  X = 378.0   Y = 183.0  Time = 1250452568864,  X = 384.0   Y = 167.0  Time = 1250452568848,  X = 384.0   Y = 160.0  Time = 1250452568840]
 Area of convex hull =  -34160.5   preimiter of hull 656.1576413855265
 
 --------------------------------------------------------------------------------
 
Final Feature vector for the FS4: 
  Feature Centroid time 1.2504525968640884E12  , Feature Centroid time difference 28319.088339222613   ,    Feature area of convexhull 34160.5   ,    Feature area of convexhull/area of symbol 1.2365344240932454   ,    Feature N.Points ConvexHull/ N. points symbol 0.15302491103202848   ,    Feature Convext Perimeter/symbol perimeter 0.556529278903672   ,    Feature  percentage of convex area to bounding box area 19.493542609351433   ,    Feature area  35519.5   ,    Feature diff area of symbol to area of bounding box 16.290771116138764   ,    Feature  Ration between w/h  0.9807692307692307   ,    Feature  Log of ration between hight and width -0.008433167536862813   , 
 Feature  Log of computed area 4.550466843684004   ,    Feature  abs of area 27626.0   ,    Feature log of  abs of area 4.441318007475848   ,    Feature  Density(length/size)  4.046853548165911   ,    Feature Mean CentroidalRadius x 272.48042704626334   ,    Feature Mean CentroidalRadius y 177.19928825622776   ,    Feature Mean t 1.2504525970626514E12   ,    Feature Mean time difference 148.69395017793593   ,    Feature Mean Radius 62.000799881019084   
  \end{scriptsize}
    \\ \hline
 Feature Vector & Appends the selected Feature FS1, FS2, FS3, FS4 & Previous Steps  & & 
 
   \begin{scriptsize}
   Feature Number of primitives 3.0   ,    Feature Number of segments 9.0   ,    Feature Line count 6.0   ,    Feature Curves Count 3.0   ,    Feature Ellipse Count 1.0   ,    Feature Intersection T type -1.0   ,    Feature Intersection L type 4.0   ,    Feature Intersection X type -1.0   ,    Feature Parallel Count 1.0   ,    Feature PerPendicular Count -1.0   ,    Feature Intersection Lines Count 4.0   ,    Feature Min Radius 1.7976931348623157E308   ,    Feature Max Radius 231.70851748053468   ,    Feature Centroid x 92.54770318021201   ,    Feature Centroid y 101.3851590106007   ,    Feature Centroid time 1.2504525968640884E12   ,    Feature Centroid time difference 28319.088339222613   ,    Feature area of convexhull 34160.5   ,    Feature area of convexhull/area of symbol 1.2365344240932454   ,    Feature N.Points ConvexHull/ N. points symbol 0.15302491103202848   ,    Feature Convext Perimeter/symbol perimeter 0.556529278903672   ,    Feature  percentage of convex area to bounding box area 19.493542609351433   ,    Feature area  35519.5   ,    Feature diff area of symbol to area of bounding box 16.290771116138764   ,    Feature  Ration between w/h  0.9807692307692307   ,    Feature  Log of ration between hight and width -0.008433167536862813   ,    Feature Zernike moments 0 158.87520185460517   ,    Feature Zernike moments 0 7.007557168632727   ,    Feature Zernike moments 1 34.26844061831789   ,    Feature Zernike moments 1 6.658086415801404   ,    Feature Zernike moments 2 85.70032052974454   ,    Feature Zernike moments 2 9.441591321498212   ,    Feature Zernike moments 3 11.73170471301825   ,    Feature Zernike moments 3 66.52997844880663   ,    Feature Zernike moments 4 20.42774127507497   ,    %Feature Zernike moments 4 10.196341027811322   ,    Feature Zernike moments 5 52.821799077785066   ,    Feature Zernike moments 5 12.078236804336935   ,    Feature Zernike moments 6 27.748912050714   ,    Feature Zernike moments 6 % 9.870152472028517   ,    Feature Zernike moments 7 26.079803494397133   ,    Feature Zernike moments 7 28.109003184347657   ,    Feature Zernike moments 8 23.32097186060531   ,    Feature Zernike moments 8 7.632681250023639   ,    Feature Zernike moments 9 6.5841386188472395   ,    Feature Zernike moments 9 51.34195037191517   ,    Feature Zernike moments 10 30.122054353503337   ,    Feature Zernike moments 10 26.902895199361584   ,    Feature Zernike moments 11 1.8295982451659387   ,    Feature Zernike moments 11 29.93196640188875   ,    Feature Zernike moments 12 64.0879253626976   ,    Feature Zernike moments 12 31.811780133580722   ,    Feature Zernike moments 13 23.614051070558084   ,    Feature Zernike moments 1    1.8043229719502216   ,    
%Feature Zernike moments 14 113.92181136864328   ,    Feature Zernike moments 14 67.26888519955787   ,    Feature Zernike moments 15 47.7397132180995   ,    Feature Zernike moments 15 31.490125533238682   ,    
Feature Zernike moments 16 10.320112066817984   ,    Feature Zernike moments 16 4.007106145033957   ,    Feature Rubine 0 -1.0   ,    Feature Rubine 1 -1.0   ,    Feature Rubine 2 477.6107201476952   ,    Feature Rubine 3 0.6368010415482491   ,    Feature Rubine 4 169.49926253526885   ,    Feature Rubine 5 0.8908593331996381   ,    Feature Rubine 6 0.454279262624981   ,    Feature Rubine 7 1179.0172885029808   ,    Feature Rubine 8 4.712388980384688   ,    Feature Rubine 9 70.80157037633609   ,    Feature Rubine 10 55.4044569978846   ,    Feature Rubine 11 9.140625   ,    Feature Rubine 12 41783.0   ,    Feature  Log of computed area 4.550466843684004   ,    Feature  abs of area 27626.0   ,    Feature log of  abs of area 4.441318007475848   ,    Feature  Density(length/size)  4.046853548165911   ,    Feature Mean CentroidalRadius x 272.48042704626334   ,    Feature Mean CentroidalRadius y 177.19928825622776   ,    Feature Mean t 1.2504525970626514E12   ,    Feature Mean time difference 148.69395017793593   ,    Feature Mean Radius 62.000799881019084   ,  
   \end{scriptsize} \\ \hline
   Classification  & SVM classifier decision & Feature Vector  &  & 
   Symbol = Clock.  
 
 \\ \hline
   
 		\end{longtable}
%}

%\end{table}

\end{scriptsize}

\end{landscape}
